Use the left-division method to solve the following set:
3x + 2y – 9z = -65
-9x-5y+2z=16
6x +Ty +3z = 5

• Solution
The matrix A is

We can use MATLAB to check the determinant of A to see whether the problem is singular.
The session looks like this:
»A = [3,2,-9;-9,-5,2;6,7,3);
»det(A)
ans
288
Because IAI i 0, a unique solution exists. It is obtained as follows:
»b = [-65;16;5);
»A\b
ans
2.0000
-4.0000
7.0000
This answer gives the vector x, which corresponds to the solution x = 2, y = -4, z = 7.
It can be checked by determining whether Ax gives the vector b, by typing
»A*ans
ans
-65.0000
16.0000
5.0000
which is the vector b. Thus the answer is correct.